The rate constant of a reaction at $500 \ K$ and $700 \ K$ are $0.02 \ s^{-1}$ and $0.2 \ s^{-1}$ respectively. The activation energy of the reaction (in $kJ \ mol^{-1}$) is $(R=8.3 \ J \ K^{-1} \ mol^{-1})$

For the reaction $A \rightleftharpoons B$,if $E_a$ is the activation energy of the forward reaction,then the activation energy of the backward reaction is:

The temperature at which the rate constants of the two gaseous reactions given below become equal is . . . . . . $K$. (Nearest integer).
$X \longrightarrow Y \quad k_1 = 10^6 e^{\frac{-30000}{T}}$
$P \longrightarrow Q \quad k_2 = 10^4 e^{\frac{-24000}{T}}$
Given: $\ln 10 = 2.303$

For a complex reaction $A \xrightarrow{K} \text{products}$,where $Ea_1 = 180 \ kJ/mol$,$Ea_2 = 80 \ kJ/mol$,and $Ea_3 = 50 \ kJ/mol$,the overall rate constant $K$ is related to individual rate constants by the equation $K = (\frac{K_1 \cdot K_2}{K_3})^{2/3}$. The activation energy $(kJ/mol)$ for the overall reaction is:

For $A + B \longrightarrow C + D$; $\Delta H = -20 \ kJ \ mol^{-1}$,the activation energy of the forward reaction is $85 \ kJ \ mol^{-1}$. The activation energy for the backward reaction is.....$kJ \ mol^{-1}$

For an endothermic reaction,where $\Delta H$ represents the enthalpy of the reaction in $kJ/mol$,the minimum value for the energy of activation will be